Gaia stellar measurements are currently revolutionizing our knowledge of the evolutionary history of the Milky Way. 3D maps of the interstellar dust provide complementary information and are a tool for a wide range of uses. We aimed at building 3D maps of the dust in the Local arm and surrounding regions. To do so, Gaia DR2 photometric data were combined with 2MASS measurements to derive extinction towards stars that possess accurate photometry and relative uncertainties on DR2 parallaxes smaller than 20%. We applied to the individual extinctions a new hierarchical inversion algorithm adapted to large datasets and to a inhomogeneous target distribution. Each step associates regularized Bayesian inversions along all radial directions and a subsequent inversion in 3D of all their results. Each inverted distribution serves as a prior for the subsequent step and the spatial resolution is progressively increased. We present the resulting 3D distribution of the dust in a 6 x 6 x 0.8 kpc 3 volume around the Sun. Its main features are found to be elongated along different directions that vary from below to above the mid-plane: the outer part of Carina-Sagittarius, mainly located above the mid-plane, the Local arm/Cygnus Rift around and above the mid-plane and the fragmented Perseus arm are oriented close to the direction of circular motion. The more than 2 kpc long spur (nicknamed the split) that extends between the Local Arm and Carina-Sagittarius, the compact near side of Carina-Sagittarius and the Cygnus Rift below the Plane are oriented along l∼40 to 55 • . Dust density images in vertical planes reveal in some regions a wavy pattern and show that the solar neighborhood within ∼500 pc remains atypical by its extent above and below the Plane. We show several comparisons with the locations of molecular clouds, HII regions, O stars and masers. The link between the dust concentration and these tracers is markedly different from one region to the other.

Aims. We aim to map the 3D distribution of the interstellar extinction of the Milky Way disc up to distances larger than those probed with the Gaia parallax alone. Methods. We applied the FEDReD (Field Extinction-Distance Relation Deconvolver) algorithm to the 2MASS near-infrared photometry together with the Gaia DR2 astrometry and photometry. This algorithm uses a Bayesian deconvolution approach, based on an empirical HR-diagram representative of the local thin disc, in order to map the extinction as a function of distance of various fields of view. Results. We analysed more than 5.6 million stars to obtain an extinction map of the entire Galactic disc within |b| < 0.24°. This map provides information up to 5 kpc in the direction of the Galactic centre and more than 7 kpc in the direction of the anticentre. This map reveals the complete shape of structures that are known locally, such as the Vela complex and the split of the local arm. Furthermore, our extinction map shows many large “clean bubbles”, especially the one in the Sagittarius-Carina complex, and four others, which define a structure that we nickname the butterfly.